Learning new alphabet
Memorizing stand-alone letters is difficult, not to mention boring. The best way, IMO, whether with book or app, is to learn a few letters and start learning some words made from them. Then more. Then some simple sentences. That's the approach taken by the book I used to learn the Arabic alphabet (ISBN 0658000772, just one of dozens of similar titles). And if I recall correctly (it's been decades), that's the approach my Russian teacher took freshman year of high school. It almost seems too obvious to mention.
(Sorry I'm late to this particular party. I've been away from Lingq for a while, and it's all Lingq's fault -- it works. I and my knowledge of Russian have been wrapped up in following world events lately.)
"Sorry I'm late to this particular party."
When I started japanese I just tried to read lyrics without romaji then listen to the song to see if they match, after that I watched some videos on youtube for the basics.
For korean I watched videos about hangul and batchim before starting reading on Lingq (since korean has more rules than japanese). Without romaji as well.
And for chinese I just picked the beginner lessons on Lingq with pinyin.
If your target langauge is not chinese or japanese and it has an actual alphabet, then you should learn the alphabet first. For Japanese you should probably learn the two alphabets that they have and for chinese you might have to learn a few hundred signs before you can read anything.
So yeah learn the writng system first and try to get rid of transliteration as fast as possible. (It is helpful for the initial learning of the script however).
The best way to learn a different alphabet or syllabary is to learn the characters using an app that allows you to practice through quizzes or spaced repetition.
You want to learn which sound each character makes, but you do not want to become overly reliant on romanisation/romaji (using the Latin alphabet to represent foreign sounds) because it will hinder your progress and lead you to not pronounce phonemes properly.
Once you have a good grasp of the characters you are learning, you can start learning the basics of the language and move on to the mini stories on Lingq.
"Do you start reading (like here in lingq) and decipher every letter until you remember it?"
For Russian, that's exactly what I did. I first looked up a basic table showing approximately how each Russian letter sounds and wrote that out by hand onto a piece of paper, and then I just started on LingQ with a simple text. It was very slow at first since every word required looking at the table several times, but it sped up very quickly. I would say within a couple of weeks I could do it without the table at all but I don't really remember.